Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labeled MC ³ by Madigan and York is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin–destination population migration flows between the 48 U.S. states and the District of Columbia during the 1990–2000 period.     

Model Uncertainty in Matrix Exponential Spatial Growth Regression Models

This article considers the most important aspects of model uncertainty for spatial regression models, namely, the appropriate spatial weight matrix to be employed and the appropriate explanatory variables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used in the regional growth literature, and develop a simple Bayesian model‐averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on previous work by reducing the computational costs through the use of Bayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial Durbin matrix exponential model has theoretical and computational advantages over the spatial autoregressive specification due to the ease of inversion, differentiation, and integration of the matrix exponential. In particular, the matrix exponential has a simple matrix determinant that vanishes for the case of a spatial weight matrix with a trace of zero. This allows for a larger domain of spatial growth regression models to be analyzed with this approach, including models based on different classes of spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants and three classes of spatial weight matrices (contiguity‐based, k‐nearest neighbor, and distance‐based spatial weight matrices), using a data set of income per capita growth for 273 European regions.     

Gaussian Process Regression and Bayesian Model Averaging: An Alternative Approach to Modeling Spatial Phenomena

Gaussian Process Regression (GPR) is a nonparametric technique that is capable of yielding reliable out‐of‐sample predictions in the presence of highly nonlinear unknown relationships between dependent and explanatory variables. But in terms of identifying relevant explanatory variables, this method is far less explicit about questions of statistical significance. In contrast, more traditional spatial econometric models, such as spatial autoregressive models or spatial error models, place rather strong prior restrictions on the functional form of relationships, but allow direct inference with respect to explanatory variables. In this article, we attempt to combine the best of both techniques by augmenting GPR with a Bayesian Model Averaging (BMA) component that allows for the identification of statistically relevant explanatory variables while retaining the predictive performance of GPR. In particular, GPR‐BMA yields a posterior probability interpretation of model‐inclusion frequencies that provides a natural measure of the statistical relevance of each variable. Moreover, while such frequencies offer no direct information about the signs of local marginal effects, it is shown that partial derivatives based on the mean GPR predictions do provide such information. We illustrate the additional insights made possible by this approach by applying GPR‐BMA to a benchmark BMA data set involving potential determinants of cross‐country economic growth. It is shown that localized marginal effects based on partial derivatives of mean GPR predictions yield additional insights into comparative growth effects across countries.     

THE IMPACT OF CRIME ON APARTMENT PRICES: EVIDENCE FROM STOCKHOLM,SWEDEN

This study uses data of about 9,000 apartment sales in Stockholm, Sweden, to assess the impact of crime on property prices. The study employs hedonic pricing modelling to estimate the impact of crime controlling for other factors (property and neighbourhood characteristics). Geographic Information System (GIS) is used to combine apartment sales by coordinates with offences, land use characteristics and demographic data of the population. The novelty of this research is threefold. First, it explores a set of land use attributes created by spatial techniques in GIS in combination with detailed geographical data in hedonic pricing modelling. Second, the effect of crime in neighbouring zones at one place can be measured by incorporating spatial lagged variables of offence rates into the model. Third, the study provides evidence of the impact of crime on housing prices in a capital city of a traditional welfare state, information otherwise lacking in the international literature. Our results indicate that apartment prices in a specific area are strongly affected by crime in its neighbouring zones, regardless of crime type. When offences were broken down by types, residential burglary, theft, vandalism, assault and robbery individually had a significant negative effect on property values. However, for residential burglary such an effect is not homogenous across space, and apartment prices in central areas are often less discounted by being exposed to crime than those in the city's outskirts.     

ESTIMATION AND HYPOTHESIS TESTING FOR NONPARAMETRIC HEDONIC HOUSE PRICE FUNCTIONS

ABSTRACT In contrast to the rigid structure of standard parametric hedonic analysis, nonparametric estimators control for misspecified spatial effects while using highly flexible functional forms. Despite these advantages, nonparametric procedures are still not used extensively for spatial data analysis due to perceived difficulties associated with estimation and hypothesis testing. We demonstrate that nonparametric estimation is feasible for large datasets with many independent variables, offering statistical tests of individual covariates and tests of model specification. We show that fixed parameterization of distance to the nearest rapid transit line is a misspecification and that pricing of access to this amenity varies across neighborhoods within Chicago.     

HEDONIC PRICING WHEN HOUSING IS ENDOGENOUS: THE VALUE OF ACCESS TO THE TRANS‐ISRAEL HIGHWAY*

Standard hedonic house pricing assumes that house prices are independent of the intangible to be priced. A methodology is proposed in which the supply as well as the demand for housing depends on the intangible. The methodology is applied to value access to the Trans‐Israel Highway (TIH). Using spatial panel data (2002–2008) we show that TIH had two effects on the housing market. It increased house prices in locations with greater access to TIH, and it affected housing construction. Standard hedonic pricing would have underestimated the value of access because it ignores the effects of housing construction on the intangible to be priced. House prices began to increase three years before TIH was inaugurated, but housing construction did not anticipate the inauguration of TIH.     

The Determinants of Regional Freight Transport: A Spatial,Semiparametric Approach

In the context of modeling regional freight the four‐stage model is a popular choice. The first stage of the model, freight generation and attraction, however, suffers from three shortcomings: first of all, it does not take spatial dependencies among regions into account, thus potentially yielding biased estimates. Second, there is no clear consensus in the literature as to the choice of explanatory variables. Second, sectoral employment and gross value added are used to explain freight generation, whereas some recent publications emphasize the importance of variables which measure the amount of logistical activity in a region. Third, there is a lack of consensus regarding the functional form of the explanatory variables. Multiple recent studies emphasize nonlinear influences of selected variables. This article addresses these shortcomings by using a spatial variant of the classic freight generation and attraction models combined with a penalized spline framework to model the explanatory variables in a semiparametric fashion. Moreover, a Bayesian estimation approach is used, coupled with a penalized Normal inverse‐Gamma prior structure, to introduce uncertainty regarding the choice and functional form of explanatory variables. The performance of the model is assessed on a real‐world example of freight generation and attraction of 258 European NUTS‐2 level regions, covering 25 European countries.     

A real options approach to amenity valuation: The role of uncertainty and risk aversion

Many empirical studies in the fields of urban and environmental economics rely on the hedonic pricing framework. This paper draws attention to two important elements that are not covered by this theory: uncertainty and relocation costs. It develops a theoretical model where agents face uncertainty, but may accumulate savings as a form of self‐insurance. It shows that uncertainty pushes up relocation costs due to the option value of waiting, while self‐insurance helps to reduce this lock‐in problem. Moreover, the model suggests that the implicit price of environmental quality increases with uncertainty even if agents are risk‐neutral.     

The Spatial Association of Demographic and Population Health Characteristics with COVID-19 Prevalence Across Districts in India

In less-developed countries, the lack of granular data limits the researcher's ability to study the spatial interaction of different factors on the COVID-19 pandemic. This study designs a novel database to examine the spatial effects of demographic and population health factors on COVID-19 prevalence across 640 districts in India. The goal is to provide a robust understanding of how spatial associations and the interconnections between places influence disease spread. In addition to the linear Ordinary Least Square regression model, three spatial regression models—Spatial Lag Model, Spatial Error Model, and Geographically Weighted Regression are employed to study and compare the variables explanatory power in shaping geographic variations in the COVID-19 prevalence. We found that the local GWR model is more robust and effective at predicting spatial relationships. The findings indicate that among the demographic factors, a high share of the population living in slums is positively associated with a higher incidence of COVID-19 across districts. The spatial variations in COVID-19 deaths were explained by obesity and high blood sugar, indicating a strong association between pre-existing health conditions and COVID-19 fatalities. The study brings forth the critical factors that expose the poor and vulnerable populations to severe public health risks and highlight the application of geographical analysis vis-a-vis spatial regression models to help explain those associations.     

RESIDENTIAL SORTING AND ENVIRONMENTAL EXTERNALITIES: THE CASE OF NONLINEARITIES AND STIGMA IN AVIATION NOISE VALUES

This paper explores the sorting process in response to differing levels of aviation noise exposure in a housing market. Spatiotemporal hedonic pricing (HP) and stated choice (SC) results reflect nonlinearities and stigma. The HP models reveal nonlinear noise depreciation increasing from 0.40 to 2.38 percent per decibel as noise increases, while the SC noise values are lower in an area with high long‐term noise exposure. These nonlinearities are attributed to the spatial sorting of noise tolerant individuals. HP results from the same “noisy” area show a “stigma” from noise during the first year after the complete removal of aviation noise.     

Human capital accumulation and long‐term income growth projections for European regions

We propose an econometric framework to construct projections for per capita income growth and human capital for European regions. Using Bayesian methods, our approach accounts for model uncertainty in terms of the choice of explanatory variables, the nature of spatial spillovers, as well as the potential endogeneity between output growth and human capital accumulation. This method allows us to assess the potential contribution of future educational attainment to economic growth and income convergence among European regions over the next decades. Our findings suggest that income convergence dynamics and human capital act as important drivers of income growth for the decades to come.     

Bayesian Spatial Filtering for Hedonic Models: An Application for the Real Estate Market

This article presents a Bayesian method based on spatial filtering to estimate hedonic models for dwelling prices with geographically varying coefficients. A Bayesian Adaptive Sampling algorithm for variable selection is used, which makes it possible to select the most appropriate filters for each hedonic coefficient. This approach explores the model space more systematically and takes into account the uncertainty associated with model estimation and selection processes. The methodology is illustrated with an application for the real estate market in the Spanish city of Zaragoza and with simulated data. In addition, an exhaustive comparison study with a set of alternatives strategies used in the literature is carried out. Our results show that the proposed Bayesian procedures are competitive in terms of prediction; more accurate results are obtained in the estimation of the regression coefficients of the model, and the multicollinearity problems associated with the estimation of the regression coefficients are solved.     

ART‐P‐MAP Neural Networks Modeling of Land‐Use Change: Accounting for Spatial Heterogeneity and Uncertainty

Spatial land‐use models over large geographic areas and at fine spatial resolutions face the challenges of spatial heterogeneity, model predictability, data quality, and of the ensuing uncertainty. We propose an improved neural network model, ART‐Probability‐Map (ART‐P‐MAP), tailored to address these issues in the context of spatial modeling of land‐use change. First, it adaptively forms its own network structure to account for spatial heterogeneity. Second, it explicitly infers posterior probabilities of land conversion that facilitates the quantification of prediction uncertainty. Extensive calibration under various test settings is conducted on the proposed model to optimize its utility in seeking useful information within a spatially heterogeneous environment. The calibration strategy involves building a bagging ensemble for training and stratified sampling with varying category proportions for experimentation. Through a temporal validation approach, we examine models’ performance within a systematic assessment framework consisting of global metrics and cell‐level uncertainty measurement. Compared with two baselines, ART‐P‐MAP achieves consistently good and stable performance across experiments and exhibits superior capability to handle the spatial heterogeneity and uncertainty involved in the land‐use change problem. Finally, we conclude that, as a general probabilistic regression model, ART‐P‐MAP is applicable to a broad range of land‐use change modeling approaches, which deserves future research.     

PRICING POLICY REACTIONS TO AGGLOMERATION IN A MARKET WITH SPATIAL SEARCH*

ABSTRACT. Price dispersion (variation) and agglomeration are common characteristics of spatial markets, in particular, markets with imperfect consumer information and search. However, pricing and location strategies in these markets are not well analyzed since spatial search is difficult to model without restricting the spatial dimension of the problem. This paper analyzes pricing and location strategies in a market with spatid search using a probabilistic modeling strategy that does not restrict search patterns in the plane. Specifically, the analysis considers the pricing strategy of an isolated firm in response to the agglomeration of competing firms. Results indicate that spatial and temporal price dispersion are effective responses to competitors'agglomeration. However, the relative effectiveness of these strategies varies with market conditions. In addition, agglomeration can have some counterintuitive effects. This paper also provides insights into existing theories of spatial search and spatial competition in spatially-restricted (linear and circular) markets.     

Applying Geostatistical Analysis to Crime Data: Car-Related Thefts in the Baltic States

Geostatistical methods have rarely been applied to area-level offense data. This article demonstrates their potential for improving the interpretation and understanding of crime patterns using previously analyzed data about car-related thefts for Estonia, Latvia, and Lithuania in 2000. The variogram is used to inform about the scales of variation in offense, social, and economic data. Area-to-area and area-to-point Poisson kriging are used to filter the noise caused by the small number problem. The latter is also used to produce continuous maps of the estimated crime risk (expected number of crimes per 10,000 habitants), thereby reducing the visual bias of large spatial units. In seeking to detect the most likely crime clusters, the uncertainty attached to crime risk estimates is handled through a local cluster analysis using stochastic simulation. Factorial kriging analysis is used to estimate the local- and regional-scale spatial components of the crime risk and explanatory variables. Then regression modeling is used to determine which factors are associated with the risk of car-related theft at different scales.     

A Spatial Price Determination Model for Multi‐Market Heterogeneously Distributed Resources: An Application to Forestry Markets in Sweden

The spatial dimension is a key paradigm in price determination, as attested by recent studies in the literature that highlighted the differential in market behavior between spatial and non‐spatial pricing settings. In this paper, we develop a model of spatial pricing for multi‐market heterogeneously distributed resources, with an application to the Swedish forestry sector. The focus of the model is to estimate the impact of spatial interaction on the demand for resources in terms of resource allocation, competition, and pricing. In its core, the pricing mechanism relies on a supply–demand framework. Using disaggregated data at the gridcell level for forest feedstock supply and harvesting costs in Sweden, we construct regional supply curves for each gridcell assuming a maximum transportation distance to delimit the potential market. Demand nodes are exogenously determined and are adjusted using a distance‐decay model to assess demand pressure across locations. We apply the model empirically to assess the impact on forest feedstock prices of a 20 TWh increase in biofuel production.     

A Note on the Mixed Geographically Weighted Regression Model*

Abstract. A mixed, geographically weighted regression (GWR) model is useful in the situation where certain explanatory variables influencing the response are global while others are local. Undoubtedly, how to identify these two types of the explanatory variables is essential for building such a model. Nevertheless, It seems that there has not been a formal way to achieve this task. Based on some work on the GWR technique and the distribution theory of quadratic forms in normal variables, a statistical test approach is suggested here to identify a mixed GWR model. Then, this note mainly focuses on simulation studies to examine the performance of the test and to provide some guidelines for performing the test in practice. The simulation studies demonstrate that the test works quite well and provides a feasible way to choose an appropriate mixed GWR model for a given data set.     

Weighted Bidimensional Regression. 加权二维回归

Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two‐dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two‐dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face‐matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation.     

THE SLX MODEL

We provide a comprehensive overview of the strengths and weaknesses of different spatial econometric model specifications in terms of spillover effects. Based on this overview, we advocate taking the SLX model as point of departure in case a well‐founded theory indicating which model is most appropriate is lacking. In contrast to other spatial econometric models, the SLX model also allows for the spatial weights matrix W to be parameterized and the application of standard econometric techniques to test for endogenous explanatory variables. This starkly contrasts commonly used spatial econometric specification strategies and is a complement to the critique of spatial econometrics raised in a special theme issue of the Journal of Regional Science (Volume 52, Issue 2). To illustrate the pitfalls of the standard spatial econometrics approach and the benefits of our proposed alternative approach in an empirical setting, the Baltagi and Li (2004) cigarette demand model is estimated.     

Hedonic pricing analysis of the influence of urban green spaces onto residential prices: the case of Leipzig,Germany

In the light of global urbanization and biodiversity loss, ecosystem services provided by urban green spaces (UGS) are becoming increasingly important, not least as a recovery and recreation opportunity for citizens. The valuation of UGS is significant for urban planners, who make decisions on the creation or removal of UGS. We analysed the influence of UGS on residential property prices in Leipzig, Germany, by applying a hedonic pricing analysis. This analysis complements the existing literature by considering both sale and rental prices for flats and houses; moreover, the shape of UGS is taken into account explicitly; finally, it is the first study in Germany to analyse UGS in hedonic studies to such an extent. The results demonstrate that the size of the nearest UGS has a stronger impact on prices compared to the distance from it. With respect to shape, we found that the simpler the UGS shape, the higher the prices. Although we find an impact of UGS on prices, the impact is smaller than that of other characteristics. The proposed valuation approach and obtained results inform urban planners regarding the design of new UGS and raise awareness about potential intended and unintended economic and social effects.